An example of Arnold diffusion for near-integrable Hamiltonians
V. Kaloshin, M. Levi, Bulletin of the American Mathematical Society 45 (2008) 409–427.

How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency
A. Gorodetski, V. Kaloshin, Advances in Mathematics 208 (2007) 710–797.

A limit shape theorem for periodic stochastic dispersion
D. Dolgopyat, V. Kaloshin, L. Koralov, Communications on Pure and Applied Mathematics 57 (2004) 1127–1158.

The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
V. Kaloshin, Inventiones Mathematicae 151 (2003) 451–512.

A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I
V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 17–27.

A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 28–36.